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The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…

Recurrence plot based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the…

Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late…

We present Link Density (LD) computed from the Recurrence Network (RN) of a time series data as an effective measure that can detect dynamical transitions in a system. We illustrate its use using time series from the standard Rossler system…

The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…

Recurrence plots and their associated quantifiers provide a robust framework for detecting and characterising complex patterns in non-linear time-series. In this paper, we employ recurrence quantification analysis to investigate the…

The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…

Observables of out-of-equilibrium quantum many-body systems display complex temporal behavior that encodes the underlying physical mechanisms but typically resists straightforward interpretations. We introduce recurrence analysis - a…

The identification of complex periodic windows in the two-dimensional parameter space of certain dynamical systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic…

Couplings in complex real-world systems are often nonlinear and scale-dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a…

Recurrence plot is a quite easy tool to be used in time series analysis,in particular for measuring unstable periodic orbits embedded in a chaotic dynamical system. Recurrence quantified analysis (RQA) is an advance tool that allows the…

Recently a method which employs computing of fluctuations in a measure of nonlinear similarity based on local recurrence properties in a univariate time series, was introduced to identify distinct dynamical regimes and transitions between…

We present a general and flexible framework for detecting regime changes in complex, non-stationary data across multi-trial experiments. Traditional change point detection methods focus on identifying abrupt changes within a single time…

Many natural systems undergo critical transitions, i.e. sudden shifts from one dynamical regime to another. In the climate system, the atmospheric boundary layer can experience sudden transitions between fully turbulent states and…

Recurrence quantification analysis (RQA) is a widely used tool for studying complex dynamical systems, but its standard implementation requires computationally expensive calculations of recurrence plots (RPs) and line length histograms.…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot based data analysis and to widen its application potential. We will give a brief overview about important and…

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…

Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…

Recurrence plots (RPs) are powerful tools for visualizing time series dynamics; however, traditional Recurrence Quantification Analysis (RQA) often relies on global metrics, such as line counting, that can overlook system-specific,…